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Reginald D. Smith

Publications and source records attributed to Reginald D. Smith.

At least 19 recordsLinked to original sources
arXiv2022

Communicating extraterrestrial intelligence (CETI) interaction models based on the Drake Equation

The Drake Equation has proven fertile ground for speculation about the abundance, or lack thereof, of communicating extraterrestrial intelligences (CETIs) for decades. It has been augmented by subsequent authors to include random variables in order to understand its probabilistic behavior. However, in most cases, the emergence and lifetime of CETIs are assumed to be independent of each other. In this paper, we will derive several expressions that can demonstrate how CETIs may relate to each other in technological age as well as how the dynamics of the concurrent CETI population change under basic models of interaction, such as the Allee Effect. By defining interaction as the change in the expected communication lifetime with respect to the density of CETI in a region of space, we can use models and simulation to understand how the CETI density can promote or inhibit the longevity and overall population of interstellar technological civilizations.

physics.gen-ph↗
arXiv2020

An improved estimate of the inverse binary entropy function

Two estimates for the inverse binary entropy function are derived using the property of information entropy to estimate combinatorics of sequences as well as related formulas from population genetics for the effective number of alleles. The second estimate shows close correspondence to the actual value of the inverse binary entropy function and can be seen as a close approximation away from low values of binary entropy where $p$ or $1-p$ are small.

cs.IT↗
arXiv2018

Bitcoin Average Dormancy: A Measure of Turnover and Trading Activity

Attempts to accurately measure the monetary velocity or related properties of bitcoin used in transactions have often attempted to either directly apply definitions from traditional macroeconomic theory or to use specialized metrics relative to the properties of the Blockchain like bitcoin days destroyed. In this paper, it is demonstrated that beyond being a useful metric, bitcoin days destroyed has mathematical properties that allow you to calculate the average dormancy (time since last use in a transaction) of the bitcoins used in transactions over a given time period. In addition, bitcoin days destroyed is shown to have another unexpected significance as the average size of the pool of traded bitcoins by virtue of the expression Little's Law, though only under limited conditions.

q-fin.TR↗
arXiv2015

A Mutual Information Approach to Calculating Nonlinearity

A new method to measure nonlinear dependence between two variables is described using mutual information to analyze the separate linear and nonlinear components of dependence. This technique, which gives an exact value for the proportion of linear dependence, is then compared with another common test for linearity, the Brock, Dechert and Scheinkman (BDS) test.

cs.IT↗
arXiv2014

A rapid algorithm to calculate joint probability matrices for joint entropies of arbitrary order

There is no closed form analytical equation or quick method to calculate probabilities based only on the entropy of a signal or process. Except in the cases where there are constraints on the state probabilities, one must typically derive the underlying probabilities through search algorithms. These become more computationally expensive as entropies of higher orders are investigated. In this paper, a method to calculate a joint probability matrix based on the entropy for any order is elaborated. With this method, only first order entropies need to be successfully calculated while the others are derived via multiplicative cascades.

cs.IT↗
arXiv2014

Malware "Ecology" Viewed as Ecological Succession: Historical Trends and Future Prospects

The development and evolution of malware including computer viruses, worms, and trojan horses, is shown to be closely analogous to the process of community succession long recognized in ecology. In particular, both changes in the overall environment by external disturbances, as well as, feedback effects from malware competition and antivirus coevolution have driven community succession and the development of different types of malware with varying modes of transmission and adaptability.

cs.CR↗
arXiv2013

Complexity in animal communication: Estimating the size of N-Gram structures

In this paper, new techniques that allow conditional entropy to estimate the combinatorics of symbols are applied to animal communication studies to estimate the communication's repertoire size. By using the conditional entropy estimates at multiple orders, the paper estimates the total repertoire sizes for animal communication across bottlenose dolphins, humpback whales, and several species of birds for N-grams length one to three. In addition to discussing the impact of this method on studies of animal communication complexity, the reliability of these estimates is compared to other methods through simulation. While entropy does undercount the total repertoire size due to rare N-grams, it gives a more accurate picture of the most frequently used repertoire than just repertoire size alone.

q-bio.PE↗
arXiv2013

Period doubling, information entropy, and estimates for Feigenbaum's constants

The relationship between period doubling bifurcations and Feigenbaum's constants has been studied for nearly 40 years and this relationship has helped uncover many fundamental aspects of universal scaling across multiple nonlinear dynamical systems. This paper will combine information entropy with symbolic dynamics to demonstrate how period doubling can be defined using these tools alone. In addition, the technique allows us to uncover some unexpected, simple estimates for Feigenbaum's constants which relate them to log 2 and the golden ratio, phi, as well as to each other.

nlin.AO↗
arXiv2012

Distinct word length frequencies: distributions and symbol entropies

The distribution of frequency counts of distinct words by length in a language's vocabulary will be analyzed using two methods. The first, will look at the empirical distributions of several languages and derive a distribution that reasonably explains the number of distinct words as a function of length. We will be able to derive the frequency count, mean word length, and variance of word length based on the marginal probability of letters and spaces. The second, based on information theory, will demonstrate that the conditional entropies can also be used to estimate the frequency of distinct words of a given length in a language. In addition, it will be shown how these techniques can also be applied to estimate higher order entropies using vocabulary word length.

cs.CL↗
arXiv2012

Information Theory and Population Genetics

The key findings of classical population genetics are derived using a framework based on information theory using the entropies of the allele frequency distribution as a basis. The common results for drift, mutation, selection, and gene flow will be rewritten both in terms of information theoretic measurements and used to draw the classic conclusions for balance conditions and common features of one locus dynamics. Linkage disequilibrium will also be discussed including the relationship between mutual information and r^2 and a simple model of hitchhiking.

q-bio.PE↗
arXiv2012

A drift formulation of Gresham's Law

In this paper we analyze Gresham's Law, in particular, how the rate of inflow or outflow of currencies is affected by the demand elasticity of arbitrage and the difference in face value ratios inside and outside of a country under a bimetallic system. We find that these equations are very similar to those used to describe drift in systems of free charged particles. In addition, we look at how Gresham's Law would play out with multiple currencies and multiple countries under a variety of connecting topologies.

q-fin.TR↗
arXiv2012

Propagation of Cascades in Complex Networks: From Supply Chains to Food Webs

A general theory of top-down cascades in complex networks is described which explains two similar types of perturbation amplifications in the complex networks of business supply chains (the `bullwhip effect') and ecological food webs (trophic cascades). The dependence of the strength of the effects on the interaction strength and covariance in the dynamics as well as the graph structure allows both explanation and prediction of widely recognized effects in each type of system.

q-bio.PE↗
arXiv2011

Five Differences Between Ecological and Economic Networks

Ecological and economic networks have many similarities and are often compared. However, the comparison is often more apt as metaphor than a direct equivalence. In this paper, five key differences are explained which should inform any analysis which compares the two.

physics.gen-ph↗
arXiv2010

Is high-frequency trading inducing changes in market microstructure and dynamics?

Using high-frequency time series of stock prices and share volumes sizes from January 2002-May 2009, this paper investigates whether the effects of the onset of high-frequency trading, most prominent since 2005, are apparent in the dynamics of the dollar traded volume. Indeed it is found in almost all of 14 heavily traded stocks, that there has been an increase in the Hurst exponent of dollar traded volume from Gaussian noise in the earlier years to more self-similar dynamics in later years. This shift is linked both temporally to the Reg NMS reforms allowing high-frequency trading to flourish as well as to the declining average size of trades with smaller trades showing markedly higher degrees of self-similarity.

q-fin.TR↗
arXiv2010

The Dynamics of Internet Traffic: Self-Similarity, Self-Organization, and Complex Phenomena

The Internet is the most complex system ever created in human history. Therefore, its dynamics and traffic unsurprisingly take on a rich variety of complex dynamics, self-organization, and other phenomena that have been researched for years. This paper is a review of the complex dynamics of Internet traffic. Departing from normal treatises, we will take a view from both the network engineering and physics perspectives showing the strengths and weaknesses as well as insights of both. In addition, many less covered phenomena such as traffic oscillations, large-scale effects of worm traffic, and comparisons of the Internet and biological models will be covered.

nlin.AO↗
arXiv2010

A note on the entropy of repetitive sequences of symmetry group permutations

The paper makes the observation that all orders of information entropy are equal in signals composed of repeating units of distinct symbols where the units can be classified as a member of a symmetry group. This leads to an improved metric for measuring the information content of higher order entropies in data such as text, signals, or genetics and another measure of similarity to compare the incremental information content across entropy orders when comparing data of different sizes and symbol sets or when comparing entire sequences.

cs.IT↗
arXiv2010

Right on time: Measuring Kuramoto model coupling from a survey of wristwatches

Using a survey of wristwatch synchronization from a randomly selected group of independent volunteers, one can model the system as a Kuramoto-type coupled oscillator network. Based on the phase data, both the order parameter and an estimated value of the coupling is derived and the possibilities for similar research to deduce topology from dynamics are discussed.

nlin.AO↗